assignments

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Learning the Modelling Language

To learn the OPL modelling language and how to use the platform (just google: "cplex opl tutorial")

The job shop scheduling problem (JSSP), may be described as follows: given n jobs, each composed of several operations that must be processed on m machines. Each operation uses one of the m machines for a fixed duration. Each machine can process at most one operation at a time. Once an operation initiates processing on a given machine it must complete processing on that machine without interruption. The operations of a given job have to be processed in a given order. The problem consists in, taking into account the precedence constraints, finding a schedule of the operations on the machines that minimizes the makespan (Cmax), that is, the finish time of the last operation completed in the schedule.

MIP Model

Write a mathematical programming model for the job shop scheduling problem.

OPL Model and testing

Write the model using the OPL Studio modelling language and test it with the set of instances from Beasley's OR-Library which are available at http://people.brunel.ac.uk/~mastjjb/jeb/orlib/files/jobshop1.txt.

Test the limitations of the model starting with the smaller instances and successively increasing the dimensions of the instances solved (which are the relevant parameters for the instances' "dimension"?)

Write a Paper on your results

• (follow the guidelines in http://www.elsevier.com/reviewers/reviewer-guidelines#conducting-a-review)

The paper should have the following structure:

• Abstract
• Introduction (including a short description of the problem and the objectives of the paper)
• The MIP model you used for the JSSP
• An analysis of the tests and results (including some KPI's on the difficulty of the instances and resolution time)
• Conclusions

Take the Job shop scheduling problem as described for the first assignment.

There are two paths you can take to work on a CP model for your problem:

use CP in OPL

use the CP library of the IBM optimization Studio in a general-purpose programming language (C++ and Java libraries are available).

You have examples for both in the documentation, you can browse the installed documentation or start :

http://pic.dhe.ibm.com/infocenter/cosinfoc/v12r6/index.jsp namely the sections under CP Optimizer > Getting Started with CP Optimizer

http://pic.dhe.ibm.com/infocenter/oplinfoc/v6r3/index.jsp namely the sections under IBM ILOG OPL V6.3 > Language and Interfaces Examples > OPL examples that use CP Optimizer (Constraint Programming) > Scheduling examples

As you already have explored the MIP model on the Beasley's OR-Library set of instances http://people.brunel.ac.uk/~mastjjb/jeb/orlib/files/jobshop1.txt, now you can compare both the solutions (to check for correctness) and the running times (to check for efficiency) of your alternative models.

An aspect to explore is the kind of constraints that will be used in CP, contrasting them with the linear constraints that you have designed for the MIP model. Note that you are not forced to linearize your model, but the CP Optimizer allows you to use basic constraints on your problem variables but also provide more powerful constraints suited to your problem. You can compare CP models using the basic and the more compact constraints on your problem instances.

Complete/adapt the paper you submitted for the MIP assignment describing your experiments and your results.